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| Keywords: Grötzsch graph.svg Very hastily drawn image of the fourth Mycielski graph Mycielski proved in 1955 that for every <math>k\ge1</math> there is a graph with chromatic number k that contains no triangle subgraphs that is whose maximal clique size is just 2 This was also proved by A A Zykov Mat Zb 24 1949 2 163-183 in Russian and by Blanche Descartes W T Tutte Amer Math Monthly 61 1954 p 352 The chromatic number of this graph is 4 A simple construction of triangle-free graphs of any chromatic number is this Start with a <math>k</math>-chromatic graph G with no triangle Take <math>k</math> copies of G Form all sets consisting of 1 node from each copy Connect the nodes in each of these sets to a new node The resulting graph is triangle-free and <math>k+1</math>-chromatic If you can make the image look better by all means do so Bkell original upload log wikitable date/time username resolution size edit summary ---- 09 37 17 December 2006 User Booyabazooka <a href http //upload wikimedia org/wikipedia/commons/5/5e/Fourth_Mycielski_graph svg ><img alt Thumbnail for version as of 09 37 17 December 2006 src http //upload wikimedia org/wikipedia/commons/thumb/5/5e/Fourth_Mycielski_graph svg/120px-Fourth_Mycielski_graph svg png width 120 height 115 border 0 /></a></td><td>480×460 8 KB <nowiki>Prettier version requested how's this </nowiki> ---- 10 33 3 July 2006 User Bkell <a href http //upload wikimedia org/wikipedia/commons/archive/5/5e/20061217093723 21Fourth_Mycielski_graph svg ><img alt Thumbnail for version as of 10 33 3 July 2006 src http //upload wikimedia org/wikipedia/commons/thumb/archive/5/5e/20061217093723 21Fourth_Mycielski_graph svg/120px-Fourth_Mycielski_graph svg png width 120 height 120 border 0 /></a></td><td>700×700 6 KB <nowiki>Very hastily drawn image of the fourth Mycielski graph Mycielski proved in 1955 that for every <math>k\ge1</math> there is a graph with chromatic number k that contains no triangle subgraphs that is whose maximal clique size is just 2 The chromati</nowiki> Grötzsch graph | ||||
